### Abstract

Aims: The initial aims were to use recently available observations of glioblastomas (as part of a previous study) that had been imaged twice without intervening treatment before receiving radiotherapy in order to obtain quantitative measures of glioma growth and invasion according to a new bio-mathematical model. The results were so interesting as to raise the question whether the degree of radio-sensitivity of each tumour could be estimated by comparing the model-predicted and actual durations of survival and total numbers of glioma cells after radiotherapy. Materials and methods: The gadolinium-enhanced T1-weighted and T2-weighted magnetic resonance imaging volumes were segmented and used to calculate the velocity of radial expansion (v) and the net rates of proliferation (ρ) and invasion/dispersal (D) for each patient according to the bio-mathematical model. Results: The ranges of the values of v, D and ρ show that glioblastomas, although clustering at the high end of rates, vary widely one from the other. The effects of X-ray therapy varied from patient to patient. About half survived as predicted without treatment, indicating radio-resistance of these tumours. The other half survived up to about twice as long as predicted without treatment and could have had a corresponding loss of glioma cells, indicating some degree of radio-sensitivity. These results approach the historical estimates that radiotherapy can double survival of the average patient with a glioblastoma. Conclusions: These cases are among the first for which values of v, D and ρ have been calculated for glioblastomas. The results constitute a 'proof of principle' by combining our bio-mathematical model for glioma growth and invasion with pre-treatment imaging observations to provide a new tool showing that individual glioblastomas may be identified as having been radio-resistant or radio-sensitive.

Original language | English (US) |
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Pages (from-to) | 301-308 |

Number of pages | 8 |

Journal | Clinical Oncology |

Volume | 20 |

Issue number | 4 |

DOIs | |

State | Published - May 1 2008 |

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### Keywords

- Bio-mathematical model
- glioblastoma
- invasion
- proliferation
- radiation therapy
- radio-sensitivity

### ASJC Scopus subject areas

- Oncology
- Radiology Nuclear Medicine and imaging

### Cite this

*Clinical Oncology*,

*20*(4), 301-308. https://doi.org/10.1016/j.clon.2008.01.006